time to travel 306 miles

Speed Distance Time Calculator

Please enter the speed and distance values to calculate the travel time in hours, minutes and seconds.

About Speed Distance Time Calculator

This online calculator tool can be a great help for calculating time basing on such physical concepts as speed and distance. Therefore, in order to calculate the time, both distance and speed parameters must be entered. For the speed , you need to enter its value and select speed unit by using the scroll down menu in the calculator. For distance , you should enter its value and also select the proper length measurement unit from the scroll down menu. You'll receive the result in standard time format (HH:MM:SS).

Time Speed Distance Formula

Distance is equal to speed × time. Time is equal Distance/Speed.

Calculate Time from Distance and Speed Examples

Recent comments.

One of the best tools I've found for the calculations.

Going 65mph for 30 seconds how far would you get? None of these formulas work without distance. How would I find the distance from time and speed?

if i travel 0.01 inches per second and I need to travel 999999999 kilometers, it takes 556722071 Days and 20:24:34 WHAT

4. How long does it take to do 100m at 3kph ? No I thought you would just divide 100 ÷ 3 = which 33.33333 so 33 seconds or so I thought. But apparently it 2 mins.

This was the best tool ive ever used that was on point from speed to distance and time Calculator

This was somewhat unhelpful as I know the time and distance, but not the speed. Would be helpful if this calculator also could solve the other two as well.

If a total distance of 2 miles is driven, with the first mile being driven at a speed of 15mph, and the second mile driven at a speed of 45 mph: What is the average speed of the full 2 mile trip?

hi sorry im newly introduced to this and i dont understand how to use it but in need to find the distance if i was travelling in the average speed of 15km/hr in 4 hours how far would i travel

D= 697 km T= 8 hours and 12 minutes S= ?

if a train is going 130 miles in 50 minutes, how fast is it going in miles per hour ??

whats the speed if you travel 2000 miles in 20hours?

How long would it take me to drive to Mars at 100 miles per hour and how much gas would I use in a 2000 Ford Mustang000000/ Also, how much CO2 would I release into the air?

great tool helped me alot

A car can go from rest to 45 km/hr in 5 seconds. What is its acceleration?

Guys how much time will a cyclist take to cover 132 METRES With a speed of 8 km/ph

@Mike Depends on how fast that actually is. For every 10 mph above 60, but below 120, you save 5 seconds a mile. But between the 30-60 area, every ten saves 10 seconds a mile (if I am remembering correctly), and every 10 between 15-30 is 20 seconds. Realistically, it isn't likely isn't worth it, unless it is a relatively straight drive with no stops, in which case you will likely go up a gear for the drive and thus improve gas efficiency for the trip. Only really saves time if it is over long trips 300+ miles (in which case, assuming you were on the interstate) that 5 seconds a mile would save you 25 minutes from the drive, making it go from 4h35m to 4h10m. For me, I have family across the U.S., so family visits are usually 900-1400 miles. Even only driving 5 above usually saves me 90-150 minutes or so (since I often have stretches where I drive on US highways which have 55 mph speed limits)

I would like to know if driving fast is worth it for short trips. If I drive 10 MPH over the speed limit for 10 miles, how much time do i save ? Is there an equation for that ?

it helps me in lot of stuff

awesome, helped me notice how long my taiga (electric seedoo) is going to last.

Drive Time Calculator to Calculate Driving Times, Trip Distances, ETAs, and More!

This free online Driving Times Calculator will calculate the number of hours and minutes it will take you to arrive at your destination based on the number of miles or kilometers you plan to drive, combined with the average speed (MPH or KMH) you expect to drive and the number and lengths of stops you expect to make.

The calculator also includes an optional Driving Distance Calculator that will calculate the distance between two cities, addresses, or points, plus map your route and give you turn-by-turn directions.

And finally, this car and truck driving time calculator will estimate your fuel costs, tell you what date and time you will arrive at your destination -- including any time zone variations, plus show you what effect driving faster or slower will have on your arrival time.

Also on the page:

• What Time To Leave Calculator
• Driving Hours Calculator

Drive Time Calculator

Calculate distance, driving times, ETA, and trip fuel-costs based on average speed and optional stops and time zones.

Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

Destination address:

Enter the address of the destination location.

After clicking the Get Distance button the address will be added to the dropdown menu and to your web browser's memory (if you browser supports Local Storage) for later use.

Note that the address you enter will be replaced by the address returned by Google Maps.

To clear a previously entered address, select it from the menu and click the Delete (X) button.

To clear all previously entered addresses, tap the Del Delete Delete All Delete All Addresses button in the button row.

Distance Calculator Button Row:

After entering the starting and destination addresses, click the Get Distance button (you may need to click a second time if map fails to appear). Once the map has appeared you can select Show Map, Show Directions, Show Both, or Show Neither.

Note that you can drag the address markers to new locations, at which time the distance, map, and directions should update automatically.

To clear all saved addresses, click the Del Delete Delete All Delete All Addresses button.

Map driving distance:

This is the driving distance according to Google Maps. For your convenience it will be added to the distance field in the Drive Time Calculator.

Map's estimated drive time:

This is the estimated drive time according to Google Maps. You can use this to compare with the results generated by the Drive Time Calculator.

Map's average speed:

This is the estimated average speed according to Google Maps. You can use this to compare with your own estimate.

Trip distance:

If you used the optional Driving Distance Calculator, and it worked correctly, this field should already be filled in. If not, enter the number of units (miles or kilometers) you plan on driving.

Average speed (MPH or KPH):

Select the average speed you plan to drive in miles per hour (MPH) or kilometers per hour (KPH).

Or, if you want to estimate travel times for speeds greater than 200 (jet, future commuter rail, Amtrak, high speed trains, etc.), enter the higher speed in the other field on this line.

Or, if one or more segements of your trip have significantly different speed limits, be sure you have entered the Trip distance in the previous row, and then tap the grid icon next to the selection menu to open the Average Speed Calculator . There you can enter up to 6 different distances, each with their own separate speed limits.

Change the distance and speed starting with the first row and working from top row to bottom row. After changing and tabbing out of one distance row, the next row will be filled-in with the total distance remaining to be allocated to a speed limit.

Once you are done allocating distances to speeds, tap the Close button at the bottom to close this mini-calculator. This will automatically set the average speed selection menu to the calculated average speed.

Departure date and time:

If you want to have the drive time calculator calculate your estimated date and time of arrival, select your departure date and time.

Optional Entries & Settings:

Click the plus (+) button to expand the optional settings. These include stop times, time zone, fuel cost, and speed comparison settings.

If you would like to adjust the drive time based on any expected stops, you can:

• Enter the total number of minutes in the far right-hand field.
• Select the number of stops and the average hours and minutes for each.
• Tap the Stops button in this row to open a custom stops form where you can customize each individual stop time (hour and minutes).

Note that changing the average hours and minutes will reset the custom stop fields to the average hours and minutes.

Compare average speed:

The results will include a chart comparing the driving and arrival times at speeds above and below the average speed you entered. Change the select menus in this row if you wish to customize the chart.

Destination time zone (DTZ):

If your trip will cover more than one time zone, select the number of hours the destination time zone is ahead or behind the time zone of the starting location.

Fuel cost factors:

If you would like the calculator to estimate your fuel cost for the trip, enter your vehicle's fuel usage rating and the cost per unit of fuel. Both fields must be filled in for the fuel cost to calculate.

MPG: Miles Per Gallon.

KPL: Kilometers Per Liter.

Drive time:

Based on your entries, this is the estimated number of hours and minutes it will take you to reach your destination.

Arrival date and time:

Based on your entries, this the estimated date and time you will arrive at your destination. If you indicated your destination is in a different time zone, this field will include the Destination Time Zone (DTZ) date and time in parenthesis.

Trip fuel cost:

If you completed the fuel related fields optional entry section of the calculator, this line will show the estimated cost of fuel for the trip.

If you would like to save the current entries and results to the device you are using, tap or click on the Data tab and then tap or click on the Save button. If you upgrade your Basic, Local Storage subscription to the Cloud Storage acess level, you can save multiple sets of entries for this calculator to the secure online database, which makes them accessable from any device.

Related Calculators

Help and tools, what time to leave calculator and a driving hours calculator., what time do i have to leave to get there on time.

Once you have used the travel time calculator on this page to get the hours and minutes of your journey, use the following calculator to estimate what time you will have to leave by to get to your destination by a specified time and date.

Note that for every hour you expect to encounter metropolitan rush hour traffic (6am to 10pm or 4pm to 8pm), you may want to add at least 1 hour to your drive time.

Actual Drive Time Calculator

Use the following calculator to total up your actual driving hours for your trip. You can enter start and stop times using am and pm or using military time (leave am/pm blank), or you can enter just the hours and minutes for each segment between stops.

If you have any suggestions for other bonus calculators for this page, please let me know using the expandable feedback form beneath the Drive Time Calculator.

Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.

Speed and Time Calculator

Search calculateme.

Mileage Calculator

Use the following mileage calculator to determine the travel distance, in terms of miles, and time taken by car to travel between two locations in the United States, disregarding traffic conditions.

Speed, Distance & Time Calculator

Use this speed calculator to easily calculate the average speed, distance travelled and the trip duration of a vehicle: car, bus, train, bike, motorcycle, plane etc. Works with miles, feet, kilometers, meters, etc..

Related calculators

• Speed, Distance & Time Calculation
• Average Speed formula
• Distance formula
• Duration (Time) formula
• How to calculate the average speed of a car?

    Speed, Distance & Time Calculation

In order to use the above speed, distance & time calculator, or do such math on your own, you will need to know two out of three metrics: speed, distance, time. You will need to convert the metrics to the same time and distance units, e.g. miles, kilometers, meters, yards, feet, and hours, minutes or seconds. For example, if you have speed in mph (miles per hour), time should also be in hours. If you have distance in kilometers, then speed should also be in km/h (kilometers per hour).

The unit of the result will depend on the units you input, but our speed calculator will conveniently display additional units where appropriate.

    Average Speed formula

The formula for average speed, also called average velocity in physics and engineering, is:

where v is the velocity, d is the distance, and t is the time, so you can read it as Speed = Distance / Time . As noted above, make sure you convert the units appropriately first, or use our speed calculator which does that automatically. The resulting unit will depend on the units for both time and distance, so if your input was in miles and hours, the speed will be in mph. If it was in meters and seconds, it will be in m/s (meters per second).

Example: If you took a plane from New York to Los Angeles and the flight was 5 hours of air time, what was the speed of the plane, given that the flight path was 2450 miles? The answer is 2450 / 5 = 490 mph (miles per hour) average speed. If you want the result in km/h, you can convert from miles to km to get 788.58 km/h.

    Distance formula

The formula for distance, if you know time (duration) and the average speed, is:

Example: If a truck travelled at an average speed of 80 km per hour for 4 hours, how many miles did it cover in that time? To find the miles covered, first, calculate 80 * 4 = 320 km, then convert km to miles by dividing by 1.6093 or by using our km to miles converter to get the answer: 198.84 miles.

    Duration (Time) formula

The time, or more precisely, the duration of the trip, can be calculated knowing the distance and the average speed using the formula:

where d is the distance travelled, v is the speed (velocity) and t is the time, so you can read it as Time = Distance / Speed . Make sure you convert the units so both their distance and time components match, or use our trip duration calculator above which will handle conversions automatically. For example, if you have distance in miles and speed in km/h, you will need to convert speed to mph or distance to kilometers. The time unit of the result will match the time unit of the speed measure, so if it is measured in something per hour, the result will be in hours. If it is measured in some unit per second, the result will be in seconds.

Example: If a train can travel 500 miles with an average speed of 50 miles per hour, how long it would take it to complete a 500-mile route? To find the answer, use the formula and substitute the values, resulting in 500 / 50 = 10 hours.

    How to calculate the average speed of a car?

Say you travelled a certain distance with a car or another vehicle and you want to calculate what its average speed was. The easiest way to do that would be by using the calculator above, but if you prefer, you can also do the math yourself. Either way, you need to know the distance to a satisfactory approximation, for which you can use a map (e.g. Google Maps) to measure the distance from point to point. Make sure you measure closely to the path you took, and not via a straight line, unless you travelled by air in which case that would be a good approximation. Of course, having a GPS reading of the distance would be more precise. Then you need to know the travel time. Make sure you subtract any rests or stops you made from the total trip duration.

If the total distance travelled was 500 miles and the time it took you was 5 hours, then your average speed was 500 / 5 = 100 miles per hour (mph). If the distance was 300 kilometers and it took you 5 hours to cover it, your speed was 300 / 5 = 60 km/h (kilometers per hour).

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Speed Distance Time Calculator" , [online] Available at: https://www.gigacalculator.com/calculators/speed-calculator.php URL [Accessed Date: 22 Jun, 2024].

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Distance and Average Speed to Travel Time Calculator

Click save settings to reload page with unique web page address for bookmarking and sharing the current tool settings

✕ clear settings

Flip tool with current settings and calculate average speed or total distance

Related Tools

• Average speed calculator
• Travel distance calculator
• Convert speed into different units
• Convert distance into different units
• Convert time duration into different units

This calculator will estimate the travel time for a journey using the travel distance to destination and the expected average speed of the method of travel.

Once a distance and speed have been entered the calculated time will be displayed in the answer box. Also a conversion scale will be generated for different values of distance versus time at the same speed.

This tool estimates the journey time with the following formula:

• d = Distance

Distance Travelled

Enter the expected distance to be travelled in any units.

Average Speed

Enter the estimated average speed of the intended method of transport.

Time Estimate

This is an estimate of the total time it will take to complete the journey without any delays.

What is TravelTime?

Travel Time Map Generator & Isochrones

I know i can get from a to b by public transport within my selected time, but it's not showing up.

If you're using public transport to do your analysis, it can look like we don't include a specific transit line. But it is rare that we have forgotten to add it! We have a full data team collecting transport data, and they're rarely caught out. It's usually due to understanding how we calculate travel time catchments. We build the area to include:

• Walking to the station platform
• Waiting for the next available departure
• Time spent boarding the train
• Giving enough time to take the A to B journey
• Depart on the station on the other side.

That means if you set your max travel time at 30 minutes, and the train journey you think should be included takes 28 minutes, it probably won't show up, because the other steps push it over the max 30 min limit. Try adding an extra 5-10 minutes to your max catchment area and see if this helps! Understand how we built our public transport model

You can't drive that far / you can drive much further than that

We recommend that you do a little experiment.

• Open another mapping app of your choice and enter an A to B route
• Select a departure time for tomorrow.

The average mapping provider gives very vague driving estimations. It's not uncommon to see a journey estimation between 30 minutes up to 2 hours. That's a lot of buffer room!

Our driving model only returns one singular best possible time estimate. We do this using our purpose-built driving model. Explore how we've built our driving model.

Still not convinced?

You can explain your data issue to us here and we can help you out. Please include in your request whether you're using the API for commercial or personal purposes.

About this tool

This demo was built to showcase the TravelTime API. To use the full capabilities of the API you will need coding skills, or experience with one of our integrations: QGIS, Alteryx or ArcGIS. Access to the API gives you larger travel time catchment areas, more transport mode options and large request volumes. Access the developer playground here.

What is a travel time map?

Our map tool allows you to create a 'How far can I go map' by transport mode and time limit. For example someone can ask how far can I drive from my home in 30 minutes. The tool outputs shapes, also known as travel time isochrones visualise where's reachable. Sometimes these shapes are incorrectly labelled as a 'travel time radius map'. A radius is always just a circular shape, but a travel time shape is completely unique as it analyses all locations reachable using a specific mode of transport.

How to create a drive time radius map or other modes

• Select a start location
• Select a maximum travel time limit
• Select a mode of transport, for example driving
• Voila! There's your driving radius map

Use cases for consumers

• Create a commute time map so you can see where to live based on commute time.
• How far can i travel in a given time: compare transport coverage for different areas.
• Create a drive time radius map: explore how far you can travel on a road trip.

Use cases for businesses

• Travel time mapping up to 4 hours & cross reference other data sets in GIS such as population data
• Site selection analysis: analyse the best location to locate a business by adding thousands of analysis points
• Create a distance matrix or travel time matrix & calculate travel times from thousands of origins to thousands of destinations
• Network analysis / travelling salesman problem: use spatial analytics to solve routing problems
• Commute time map - plot thousands of employee commute times for an office relocation

This web page is a limited demo that can do the following:

• Create up to 3 time polygons visualising where's reachable within 2 hours or less. Our API can create large travel time areas, talk to sales.
• Calculate travel times from an origin to various points of interest - in this demo we use points from Foursquare Give A to B routing details

Full access

We provide full analysis by all transport modes and all travel time areas in our full service. You can access this by:

• Book a demo
• Trial TravelTime API
• Trial QGIS Plugin
• Trial ArcGIS Pro Add-In
• Trial Alteryx Macros

Problem with the data?

Create a Travel Time Map

Draw a travel time area or make your own commute time map.

• See 'How far can I get' in X minutes
• Create a drive time map or any other transport mode
• Overlap many shapes & highlight overlap area
• Search points of interest within the area
• Get A to B routing details

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Speed Distance Time Calculator

Initially, this amazing calculator was developed especially for athletes, cyclists or joggers. However, all people who are required due to their activities to calculate an unknown variable with the help of the other two variables, will find use in it. You can use it in two ways. First, enter two particular variables in order to find the third one. Second, you may find the variable by entering the details.

Time can be entered as hh:mm:ss , mm:ss or ss (hh=hours mm=minutes ss=seconds).

Example Time Formats:

• 1:20:45 = 1 hour, 20 minutes and 45 seconds
• 18:25 = 18 minutes and 25 seconds
• 198 = 198 seconds = 3 minutes and 18 seconds

Speed: miles yards feet inches kilometers meters centimeters per hour minute second

Distance: miles yards feet inches kilometers meters centimeters millimeters

You may set the number of decimal places in the online calculator. By default there are only two decimal places.

0 1 2 3 4 5 6 7 8 9 Decimal Places

Speed    miles/hr miles/min miles/sec yards/hr yards/min yards/sec feet/hr feet/min feet/sec inch/hr inch/min inch/sec km/hr km/min km/sec meter/hr meter/min meter/sec cm/hr cm/min cm/sec mm/hr mm/min mm/sec

Distance    miles yards feet inches kilometers meters centimeters millimeters

Time (hh:mm:ss)

This calculator includes the following algorithms:

Speed = Distance divided by Time

Distance = Speed multiplied by Time

Time = Distance divided by Speed

You may also be interested in our Running Pace Calculator or Steps to Miles Calculator

• Currently 4.18/5

Rating: 4.2 /5 (257 votes)

• Inverse percentage calculator
• CO2 Emission

Travel Time Calculator

Faq about travel time.

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How long would it take to drive 170 miles? | Speed to Time Calculator

How long would it take to drive 170 miles? Use the calculator below to find how much time it will take to drive, sail, run or walk a given distance at the speed you choose.

Speed to Time Calculator

Short answer:, detailed answer:.

• Speed Units Converter

Similar Questions Answered by This Calculator

How much time to cover 170 miles?

At 60 miles per hour, how long does it take to travel 170 miles?

How long is 170 mi in time?

Sample Speed to Time Conversions

• Time to drive 4600 mi at 55 mi/h
• Time to drive 91 mi at 45 mi/h
• Time to drive 2750 mi at 30 mi/h
• Time to drive 530 mi
• Time to drive 960 mi at 30 mi/h
• Time to drive 670 mi at 30 mi/h
• Time to drive 18 mi
• Time to drive 38 mi
• Time to drive 2850 mi

While every effort is made to ensure the accuracy of the information provided on this website, neither this website nor its authors are responsible for any errors or omissions. Therefore, the contents of this site are not suitable for any use involving risk to health, finances or property.

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Orbits and Kepler’s Laws

Kepler's Laws of Planetary Motion

The story of how we understand planetary motion could not be told if it were not for the work of a German mathematician named Johannes Kepler. 

Kepler's three laws describe how planets orbit the Sun. They describe how (1) planets move in elliptical orbits with the Sun as a focus, (2) a planet covers the same area of space in the same amount of time no matter where it is in its orbit, and (3) a planet’s orbital period is proportional to the size of its orbit.

Who Was Johannes Kepler?

Johannes Kepler was born on Dec. 27, 1571, in Weil der Stadt, Württemberg, which is now in the German state of Baden-Württemberg.

As a rather frail young man, the exceptionally talented Kepler turned to mathematics and the study of the heavens early on. When he was six, his mother pointed out a comet visible in the night sky. When Kepler was nine, his father took him out one night under the stars to observe a lunar eclipse. These events both made a vivid impression on Kepler's youthful mind and turned him toward a life dedicated to astronomy.

Kepler lived and worked in Graz, Austria, during the tumultuous early 17th century. Due to religious and political difficulties common during that era, Kepler was banished from Graz on Aug. 2, 1600. 

Fortunately, he found work as an assistant to the famous Danish astronomer Tycho Brahe (usually referred to by his first name) in Prague. Kepler moved his family from Graz, 300 miles (480 kilometers) across the Danube River to Tycho's home.

Kepler and the Mars Problem

Tycho was a brilliant astronomer. He is credited with making the most accurate astronomical observations of his time, which he accomplished without the aid of a telescope. He had been impressed with Kepler’s studies in an earlier meeting. 

However, some historians think Tycho mistrusted Kepler, fearing that his bright young intern might eclipse him as the premier astronomer of his day. Because of this, he only let Kepler see part of his voluminous collection of planetary data.

Tycho assigned Kepler the task of understanding the orbit of the planet Mars. The movement of Mars was problematic – it didn’t quite fit the models as described by Greek philosopher and scientist Aristotle (384 to 322 B.C.E.) and Egyptian astronomer Claudius Ptolemy (about 100 C.E to 170 C.E.). Aristotle thought Earth was the center of the universe, and that the Sun, Moon, planets, and stars revolved around it. Ptolemy developed this concept into a standardized,  geocentric model (now known as the Ptolemaic system) based around Earth as a stationary object, at the center of the universe.

Historians think that part of Tycho’s motivation for giving the Mars problem to Kepler was Tycho's hope that it would keep Kepler occupied while Tycho worked to perfect his own theory of the solar system. That theory was based on a geocentric model, modified from Ptolemy's, in which the planets Mercury, Venus, Mars, Jupiter, and Saturn all orbit the Sun, which in turn orbits Earth. 

As it turned out, Kepler, unlike Tycho, believed firmly in a model of the solar system known as the heliocentric model, which correctly placed the Sun at its center. This is also known as the Copernican system, because it was developed by astronomer Nicolaus Copernicus (1473-1543). But the reason Mars' orbit was problematic was because the Copernican system incorrectly assumed the orbits of the planets to be circular.

Like many philosophers of his era, Kepler had a mystical belief that the circle was the universe’s perfect shape, so he also thought the planets’ orbits must be circular. For many years, he struggled to make Tycho’s observations of the motions of Mars match up with a circular orbit.

Kepler eventually realized that the orbits of the planets are not perfect circles. His brilliant insight was that planets move in elongated, or flattened, circles called ellipses. 

The particular difficulties Tycho had with the movement of Mars were due to the fact that its orbit was the most elliptical of the planets for which he had extensive data. Thus, in a twist of irony, Tycho unwittingly gave Kepler the very part of his data that would enable his assistant to formulate the correct theory of the solar system.

Basic Properties of Ellipses

Since the orbits of the planets are ellipses, it might be helpful to review three basic properties of an ellipse:

• An ellipse is defined by two points, each called a focus, and together called foci. The sum of the distances to the foci from any point on the ellipse is always a constant. 
• The amount of flattening of the ellipse is called the eccentricity. The flatter the ellipse, the more eccentric it is. Each ellipse has an eccentricity with a value between zero (a circle), and one (essentially a flat line, technically called a parabola).
• The longest axis of the ellipse is called the major axis, while the shortest axis is called the minor axis. Half of the major axis is termed a semi-major axis. 

After determining that the orbits of the planets are elliptical, Kepler formulated three laws of planetary motion, which accurately described the motion of comets as well.

Kepler's Laws

In 1609 Kepler published “Astronomia Nova,” which explained what are now called Kepler's first two laws of planetary motion. Kepler had noticed that an imaginary line drawn from a planet to the Sun swept out an equal area of space in equal times, regardless of where the planet was in its orbit. If you draw a triangle from the Sun to a planet’s position at one point in time and its position at a fixed time later, the area of that triangle is always the same, anywhere in the orbit. 

For all these triangles to have the same area, the planet must move more quickly when it’s near the Sun, but more slowly when it is farther from the Sun. This discovery became Kepler’s second law of orbital motion, and led to the realization of what became Kepler’s first law: that the planets move in an ellipse with the Sun at one focus point, offset from the center. 

In 1619, Kepler published “Harmonices Mundi,” in which he describes his "third law." The third law shows that there is a precise mathematical relationship between a planet’s distance from the Sun and the amount of time it takes revolve around the Sun.

Here are Kepler’s Three Laws:

Kepler's First Law : Each planet's orbit about the Sun is an ellipse. The Sun's center is always located at one focus of the ellipse. The planet follows the ellipse in its orbit, meaning that the planet-to-Sun distance is constantly changing as the planet goes around its orbit.

Kepler's Second Law: The imaginary line joining a planet and the Sun sweeps out – or covers – equal areas of space during equal time intervals as the planet orbits. Basically, the planets do not move with constant speed along their orbits. Instead, their speed varies so that the line joining the centers of the Sun and the planet covers an equal area in equal amounts of time. The point of nearest approach of the planet to the Sun is called perihelion. The point of greatest separation is aphelion, hence by Kepler's second law, a planet is moving fastest when it is at perihelion and slowest at aphelion.

Kepler's Third Law: The orbital period of a planet, squared, is directly proportional to the semi-major axes of its orbit, cubed. This is written in equation form as p 2 =a 3 . Kepler's third law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit. Mercury, the innermost planet, takes only 88 days to orbit the Sun. Earth takes 365 days, while distant Saturn requires 10,759 days to do the same.  

How We Use Kepler’s Laws Today

Kepler didn’t know about gravity, which is responsible for holding the planets in their orbits around the Sun, when he came up with his three laws. But Kepler’s laws were instrumental in Isaac Newton’s development of his theory of universal gravitation, which explained the unknown force behind Kepler's third law. Kepler and his theories were crucial in the understanding of solar system dynamics and as a springboard to newer theories that more accurately approximate planetary orbits. However, his third law only applies to objects in our own solar system. 

Newton’s version of Kepler’s third law allows us to calculate the masses of any two objects in space if we know the distance between them and how long they take to orbit each other (their orbital period). What Newton realized was that the orbits of objects in space depend on their masses, which led him to discover gravity.

Newton’s generalized version of Kepler’s third law is the basis of most measurements we can make of the masses of distant objects in space today. These applications include determining the masses of moons orbiting the planets, stars that orbit each other, the masses of black holes (using nearby stars affected by their gravity), the masses of exoplanets (planets orbiting stars other than our Sun), and the existence of mysterious dark matter in our galaxy and others.

In planning trajectories (or flight plans) for spacecraft, and in making measurements of the masses of the moons and planets, modern scientists often go a step beyond Newton. They account for factors related to Albert Einstein’s theory of relativity, which is necessary to achieve the precision required by modern science measurements and spaceflight. 

However, Newton’s laws are still accurate enough for many applications, and Kepler’s laws remain an excellent guide for understanding how the planets move in our solar system.

Johannes Kepler died Nov. 15, 1630, at age 58. NASA's Kepler space telescope was named for him. The spacecraft launched March 6, 2009, and spent nine years searching for Earth-like planets orbiting other stars in our region of the Milky Way. The Kepler space telescope left a legacy of more than 2,600 planet discoveries from outside our solar system, many of which could be promising places for life.

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Tracking the Remnants of Alberto

By William B. Davis, Madison Dong, Judson Jones, John Keefe, and Bea Malsky

The remnants of Alberto were over Mexico Thursday afternoon Mexico Central Time, according to the National Hurricane Center.

The system had sustained wind speeds of 30 miles per hour.

Where did it rain?

Tropical cyclones typically drop large amounts of rain along and near the storm's path. The slower and more significant the storm’s size, the higher the likelihood of higher rainfall totals. Some storms can drop well over 30 inches of rainfall, like when Hurricane Harvey dropped over 60 inches near Nederland, Texas, in 2017.

What did the storm look like from above?

Satellite imagery can help determine the strength, size and cohesion of a storm. The stronger a storm becomes, the more likely an eye will form in the center. When the eye looks symmetrical, that often means the storm is not encountering anything to weaken it.

Alberto is the first named storm to form in the Atlantic in 2024.

In late May, the National Oceanic and Atmospheric Administration predicted that there would be 17 to 25 named storms this year, an above-normal amount.

This season follows an overly active year, with 20 named storms — including an early storm later given the official name of “Unnamed.” It was the eighth year in a row to surpass the average of 14 named storms. Only one hurricane, Idalia, made landfall in the United States.

Typically, the El Niño pattern that was in force last season would have suppressed hurricanes and reduced the number of storms in a season. But in 2023, the warm ocean temperatures in the Atlantic blunted El Niño’s usual effect of thwarting storms.

The warm ocean temperatures that fueled last year’s season returned even warmer at the start of this season, raising forecasters’ confidence that there would be more storms this year. The heightened sea surface temperatures could also strengthen storms more rapidly than usual.

To make matters worse, the El Niño pattern present last year is also diminishing, most likely creating a more suitable atmosphere for storms to form and intensify.

Hurricanes need a calm environment to form, and, in the Atlantic, a strong El Niño increases the amount of wind shear — a change in wind speed and/or direction with height — which disrupts a storm's ability to coalesce. Without El Niño this year, clouds are more likely to tower to the tall heights needed to sustain a powerful cyclone.

Sources and notes

Tracking map Source: National Hurricane Center | Notes: The map shows probabilities of at least 5 percent. The forecast is for up to five days, with that time span starting up to three hours before the reported time that the storm reaches its latest location. Wind speed probability data is not available north of 60.25 degrees north latitude.

Wind arrivals table Sources: New York Times analysis of National Hurricane Center data (arrival times); U.S. Census Bureau and Natural Earth (geographic locations); Google (time zones) | Notes: The table shows predicted arrival times of damaging, 58 m.p.h. winds in select cities when there is a chance such winds could reach those locations. “Earliest possible” times are times when, if damaging winds do arrive, there is at least a 10 percent chance they will arrive at the time shown. “Most likely” times are times when, if damaging winds do arrive, there is an equal chance that such winds will arrive before and after the time shown.

Radar map Source: National Oceanic and Atmospheric Administration via Iowa State University | Notes: These mosaics are generated by combining the 130+ individual RADARs that comprise the NEXRAD network.

Storm surge map Source: National Hurricane Center | Notes: The actual areas that could become flooded may differ from the areas shown on this map. This map accounts for tides, but not waves and not flooding caused by rainfall. The map also includes intertidal areas, which routinely flood during typical high tides.

Satellite map Source: National Oceanic and Atmospheric Administration| Notes: Imagery only updates between sunrise and sunset of the latest storm location.

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