if you were stationary in space at the same distance from the sun as the eath is, how much force would the sun be exerting on you? what would be your acceleration towrd the sun? what would be the sun's acceleration toward you?

Question

if you were stationary in space at the same distance from the sun as the eath is, how much force would the sun be exerting on you? what would be your acceleration towrd the sun? what would be the sun's acceleration toward you?

okay so im a little confused where to go with this, i have what the force of the sun exerting on me would be.
Fg=G M1M2/r^2
Fme= 6.7x10^-11((68kg)(2x10^30kg))/(1.5x10^11m)^2
fme=.403N

for the acceleration i would either need a time
a=4pi^2r/T^2
or i would need a velocity
a=v^2/r

but it says im stationary in space, do i assume that i am orbiting the sun at the same distance that the earth does and use one year as my time?

i do have another formula but i don't see how either of these will get me both the accelerations
Fg=Fw
G*M1M2/r^2=Mg Mg=a
that would still only be one acceleration
need some hints here please

Answer 1

To determine the force exerted by the sun on you when you are stationary in space at the same distance from the sun as the Earth, you can use Newton's law of universal gravitation:

Fg = G * (m1 * m2) / r²

Where:
- Fg is the force of gravitation
- G is the gravitational constant (6.7 x 10⁻¹¹ N m²/kg²)
- m1 is the mass of one object (in this case, the mass of the sun, which is approximately 2 x 10³⁰ kg)
- m2 is the mass of the other object (your mass, which you've mentioned as 68 kg)
- r is the distance between the center of the sun and your position (1.5 x 10¹¹ m)

Plugging in the values:

Fg = (6.7 x 10⁻¹¹ N m²/kg²) * ((68 kg) * (2 x 10³⁰ kg)) / (1.5 x 10¹¹ m)²
Fg ≈ 5.026 x 10²³ N

So, the force exerted by the sun on you would be approximately 5.026 x 10²³ N.

Now, let's consider the accelerations. Since you are stationary and not moving, your acceleration towards the sun would be zero. This is because acceleration is defined as the rate of change of velocity, and since you are not moving, your velocity is constant, resulting in zero acceleration.

Similarly, since the sun is much more massive than you, its acceleration towards you would also be negligible. This is because the acceleration of each object due to the gravitational force is inversely proportional to their mass. Since the sun's mass is so much larger than yours, its acceleration towards you would essentially be zero.

Therefore, both your acceleration towards the sun and the sun's acceleration towards you would be close to zero in this scenario.