Acceleration due to gravity for a hypothetical planet

In summary, when calculating the acceleration due to gravity on a hypothetical planet with the same mass as Earth but a radius of 2.5 times that of Earth, the correct formula to use is g=GM/r^2, where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet. However, it is important to use the correct values for the radius, which is 6.38 x 10^6 meters or 6,380 km, not 6.38 x 10^4 meters or 63,800 km. With the correct values, the acceleration due to gravity near the surface of the planet is approximately 1.
  • #1
balletgirl
36
0

Homework Statement


A hypothetical planet has a radius 2.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

R(earth)= 6.38 x 10^4 m
M(earth)= 5.98 x 10^24 kg
G= 6.67 x 10^-11

Homework Equations


g=GM/r^2


The Attempt at a Solution


I did: (6.67 x 10^-11)(5.98 x 10^24kg) / [2.5(6.38 x 10^4m)]^2
and got 15,708, but know this is wrong since the answer is near only 15.
 
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  • #2
The radius of Earth that you have looks like it's supposed to be kilometers.

Edit: Actually, no because Earth's radius is actually 6378 km so the exponent is just messed up.
 
  • #3
Okay I just looked it up, the radius in km is 6.38 x 10^4, and the radius in meters is 6.38 x 10^6.

I used this instead and it worked! Thank you for pointing this out for me, and the answer was actually 1.5 m/s^2, not 15.
 
  • #4

1. What is acceleration due to gravity?

Acceleration due to gravity is the acceleration that an object experiences due to the gravitational force exerted by a massive body. It is a measure of how quickly an object's velocity changes as it falls towards the surface of a planet or other celestial body.

2. How is acceleration due to gravity calculated?

The acceleration due to gravity for a hypothetical planet can be calculated using the formula a = GM/r^2, where G is the gravitational constant, M is the mass of the planet, and r is the distance from the center of the planet to the object.

3. Will the acceleration due to gravity be the same on all parts of the planet?

No, the acceleration due to gravity varies on different parts of a planet due to variations in the planet's mass and shape. For example, the acceleration due to gravity at the poles of a planet may be slightly different from the acceleration at the equator.

4. How does the acceleration due to gravity affect the motion of objects on a hypothetical planet?

The acceleration due to gravity affects the motion of objects by causing them to accelerate towards the planet's surface. This means that objects will fall towards the planet at a faster rate than they would on a planet with a lower acceleration due to gravity.

5. Can the acceleration due to gravity of a hypothetical planet be changed?

Yes, the acceleration due to gravity of a hypothetical planet can be changed by altering the planet's mass or radius. For example, if the mass of the planet were to increase, the acceleration due to gravity would also increase.

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