What is the Force Exerted by the Sun on Earth?

[tag16]

Homework Statement

The orbital speed of Earth about the Sun is 2.8x10^4 m/s and its distance from the Sun is 1.5x10^11 m. The mass of Earth is approximately 6.2x10^24 kg and that of the Sun is 2.0x10^30 kg. What is the magnitude of the force exerted by the Sun on Earth?

Homework Equations

F= Gm1m2/r^2 and F=mv^2/r

The Attempt at a Solution

I know I need to use Newtons 2nd Law but every time I plug the numbers in I get the wrong answer. I tried using F= Gm1m2/r^2 and F=mv^2/r

 

[RoyalCat]

What's the text-book answer that's making you think you're doing it wrong?
You can solve this question in two different ways, and for both, there would be redundant data.

Well, since you were already on the right track already, I'll just show you what I got when I plugged the numbers in myself.

If you know that the force the sun exerts on the Earth is gravity, then you can simply use:

|F| = GM_EM_S/R² = (6.67*6.2*2)/1.5² * 10^(-11+24+30-22) = 36.75*10^21 N

If you don't know that the force is gravity, however, but do know that the Earth revolves around the sun is an approximately circular orbit, you can say that the magnitude of the force the sun exerts upon it is:
|F| = M_E*V²/R = 6.2*2.8²/1.5 * 10^(24+8-11) = 32.40*10^21 N

We need to explain the discrepancy here somehow, though. I'd chalk it up to poor approximations of the sun's mass (Note how the centripetal force equation does not directly use the data about the mass of the sun) and the fact that the Earth orbits the sun in an elliptic orbit, and not a circular one.